Question

Where would the number $\sqrt{3}$ lie on the number line?

• A. between 0 and 1
• B. between 1 and 2
• C. between 2 and 3
• D. None of the above

Answer 1

The correct option is B

between 1 and 2

We know that when $a<b<c$, then $a^2<b^2<c^2$
Thus, the converse must be true. i.e., when $a^2<b^2<c^2$, then $a<b<c$.
Now, we know that $1<3<4$. Hence, $\sqrt{1}<\sqrt{3}<\sqrt{4}$ (When we consider the positive values of square roots)
Thus, $1<\sqrt{3}<2$. Hence, $\sqrt{3}$ lies between $1$ and $2$.